Geodesic
Local solvability and blowup of the~solution of the~Rosenau--B\"urgers equation with different boundary conditions
Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 1, pp. 93-110

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We consider several models of initial boundary-value problems for the Rosenau–Bürgers equation with different boundary conditions. For each of the problems, we prove the unique local solvability in the classical sense, obtain a sufficient condition for the blowup regime, and estimate the time of the solution decay. The proof is based on the well-known test-function method.
Keywords: blowup regime, local solvability, noncontinuable solution
Mots-clés : Rosenau–Bürgers equation. 
@article{TMF_2013_177_1_a3,
     author = {A. A. Panin},
     title = {Local solvability and blowup of the~solution of {the~Rosenau--B\"urgers} equation with different boundary conditions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {93--110},
     publisher = {mathdoc},
     volume = {177},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_177_1_a3/}
}
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A. A. Panin. Local solvability and blowup of the~solution of the~Rosenau--B\"urgers equation with different boundary conditions. Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 1, pp. 93-110. http://geodesic.mathdoc.fr/item/TMF_2013_177_1_a3/